Although this idealized parallel process has been discovered for over half a century [1]},
little has been know about how we can implement it correctly and efficiently in a parallel computer.
A major obstacle for this is a classical conundrum in concurrency:
If two adjacent sites concurrently read each other's current spin and then use that information to update themselves,
then
it will cause incorrect simulation of the process, because such concurrent update and especially the dependency relation it causes,
do not exist in the continuous-time process.
But if we avoid the concurrent adjacent updates,
then we have to pay an extra factor of degree \(\Delta \)  (in fact, chromatic number \(\chi \) ) in the time complexity for simulating the process,
which can be very large for general graph \(G\) .
